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Beliebt Rechnen >

derivative of x^5sin(2x)

Lösung

\frac{d}{d x} (x^{5} sin (2 x))

Lösung

5 x^{4} sin (2 x) + cos (2 x) \cdot 2 x^{5}

Schritte zur Lösung

\frac{d}{d x} (x^{5} sin (2 x))

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x^{5}, g = sin (2 x)

= \frac{d}{d x} (x^{5}) sin (2 x) + \frac{d}{d x} (sin (2 x)) x^{5}

\frac{d}{d x} (x^{5}) = 5 x^{4}

\frac{d}{d x} (sin (2 x)) = cos (2 x) \cdot 2

= 5 x^{4} sin (2 x) + cos (2 x) \cdot 2 x^{5}

Graph

Beliebte Beispiele

derivative of (x^2(x+1^2)/(sqrt(x-1)))

\frac{d}{d x} (\frac{x ^{2} ( x + 1 ) ^{2}}{x - 1})

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derivative of e^{y-ln(x})

\frac{d}{d x} (e^{y - l n (x)})

derivative of (x^4/(sqrt(x^5+3)))

\frac{d}{d x} (\frac{x ^{4}}{x ^{5} + 3})

(\partial)/(\partial y)(3x+y)

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